freakonomics

7–7 WRESTLER’S PREDICTED WIN
PERCENTAGE AGAINST 9–5
OPPONENT
47.2 73.4
7–7 WRESTLER’S ACTUAL WIN
PERCENTAGE AGAINST 9–5
OPPONENT
As suspicious as this looks, a high winning percentage alone isn’t enough to prove that a
match is rigged. Since so much depends on a wrestler’s eighth win, he should be
expected to fight harder in a crucial bout. But perhaps there are further clues in the data
that prove collusion.
It’s worth thinking about the incentive a wrestler might have to throw a match. Maybe he
accepts a bribe (which would obviously not be recorded in the data). Or perhaps some
other arrangement is made between the two wrestlers. Keep in mind that the pool of elite
sumo wrestlers is extraordinarily tight-knit. Each of the sixty-six elite wrestlers fights
fifteen of the others in a tournament every two months. Furthermore, each wrestler
belongs to a stable that is typically managed by a former sumo champion, so even the
rival stables have close ties. (Wrestlers from the same stable do not wrestle one another.)
Now let’s look at the win-loss percentage between the 7–7 wrestlers and the 8–6
wrestlers the next time they meet, when neither one is on the bubble. In this case, there is
no great pressure on the individual match. So you might expect the wrestlers who won
their 7–7 matches in the previous tournament to do about as well as they had in earlier
matches against these same opponents—that is, winning roughly 50 percent of the time.
You certainly wouldn’t expect them to uphold their 80 percent clip.
As it turns out, the data show that the 7–7 wrestlers win only 40 percent of the rematches.
Eighty percent in one match and 40 percent in the next? How do you make sense of that?
The most logical explanation is that the wrestlers made a quid pro quo agreement: you let
me win today, when I really need the victory, and I’ll let you win the next time. (Such an
arrangement wouldn’t preclude a cash bribe.) It’s especially interesting to note that by the
two wrestlers’ second subsequent meeting, the win percentages revert to the expected
level of about 50 percent, suggesting that the collusion spans only two matches.
And it isn’t only the individual wrestlers whose records are suspect. The collective
records of the various sumo stables are similarly aberrational. When one stable’s
wrestlers fare well on the bubble against wrestlers from a second stable, they tend to do
especially poorly when the second stable’s wrestlers are on the bubble. This indicates that
some match rigging may be choreographed at the highest level of the sport—much like
the Olympic skating judges’ vote swapping.
No formal disciplinary action has ever been taken against a Japanese sumo wrestler for
match rigging. Officials from the Japanese Sumo Association typically dismiss any such
charges as fabrications by disgruntled former wrestlers. In fact, the mere utterance of the